<p>The area bounded by \(y=(x-1)(x-3)\) and the \(x\)-axis is: [MAU049]</p>
Step-by-Step Solution
Key Concept: The parabola is negative between its roots x=1,3. Area = -\int_1^3(x-1)(x-3)dx = -\int_1^3(x^2-4x+3)dx.
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<p>$y=(x-1)(x-3)=x^2-4x+3$. Roots at $x=1,3$. Below x-axis on $[1,3]$.</p>
<p>$$A=-\int_1^3(x^2-4x+3)dx=-\left[\frac{x^3}{3}-2x^2+3x\right]_1^3$$</p>
<p>$=-[(9-18+9)-(\frac{1}{3}-2+3)]=-[0-\frac{4}{3}]=\frac{4}{3}$</p>
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Correct Answer: ['B']